An undercover sting operation has caught 76 city stores selling alcohol to minors, The Post has learned.

“This investigation should put stores that sell alcohol to minors on notice: If you break the law, we will catch you,” Gov. Cuomo said.

The State Liquor Authority used volunteer minors accompanied by agency supervisors to target 250 stores from Oct. 3 through Oct. 11.

The underage buyers were able to purchase booze at 76 of them, or nearly a third.

Merchants face fines of up to $10,000 per violation and repeat offenders could have their licenses revoked or suspended. First-time violators get slapped with fines of at least $2,500.

Some of the stores are in the city’s most fashionable neighborhoods, including Battery Park City, Brownstone Brooklyn, hipster Williamsburg and Kew Gardens in Queens.

One of the stores was Ziad’s Gourmet at 143 Smith St. in Brooklyn.

The cashier, who asked not to be identified, denied the offense.

“I’ve worked here more than 25 years and we never sell alcohol to minors,” he said. “We got a letter in April saying we sold alcohol to a minor in February.’’ He said the store was fined $2,500.

Next door, at Smith’s Grocery, the clerk said the ticket was the store’s first.

“We never got a ticket,’’ he said. “If you are government, then after we break the law, you should identify yourself and write a ticket then. Not two months later, with some letter.

“This kid was 6-foot-3. You’re telling me now that he’s underage?’’

Neighbors had mixed reactions.

Mac Scherwood, 31, a prop master for films, said, “I’m from the sticks, from Unadilla, New York.

“Where I’m from, underage drinking is a cottage industry. But the big risk upstate is underage drinking and driving, and here, there’s really not much of a risk for that. I’m not saying I condone it, but there shouldn’t be full enforcement.

“What’s funny is that I get carded by those delis constantly.”

Veronica Brown, a child-care worker, was outraged.

“Some people don’t give a s–t who they sell to. But minors need to be minors. I wouldn’t sell cigarettes or beer to kids,’’ she said. “When you do that, you’re telling a child it’s OK.”